Simply the best answers.

How to compute the integral of a variable along a line using UDF in FLUENT?

Line surfaces in FLUENT have area in 2d and 2d-axi but not in 3d, so currently integrals on line surfaces are zero.

This solution provides a sample User Defined Function (UDF) that shows how to calculate the integral of a variable (say temperature) along a line in fluent, then divide it by the length of the line, and output this number at every time step, for a large number of lines in a transient 3d simulation.

/*sample UDF code to work with for line integration: you will need to augment it to use it with multiple lines, etc*/

/* UDF to calculate line integral and line lenght weighted average of a variable.
by sra and fm 5/05

To have line integral and line average of variable V on a line S u need to
Go to Contour panel and do compute of V on S
This will fill the values necessary for computation. */